Euler's Pioneering Equation

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Publisher : Oxford University Press
ISBN 13 : 0192514067
Total Pages : 200 pages
Book Rating : 4.1/5 (925 download)

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Book Synopsis Euler's Pioneering Equation by : Robin Wilson

Download or read book Euler's Pioneering Equation written by Robin Wilson and published by Oxford University Press. This book was released on 2018-02-22 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1988 The Mathematical Intelligencer, a quarterly mathematics journal, carried out a poll to find the most beautiful theorem in mathematics. Twenty-four theorems were listed and readers were invited to award each a 'score for beauty'. While there were many worthy competitors, the winner was 'Euler's equation'. In 2004 Physics World carried out a similar poll of 'greatest equations', and found that among physicists Euler's mathematical result came second only to Maxwell's equations. The Stanford mathematician Keith Devlin reflected the feelings of many in describing it as "like a Shakespearian sonnet that captures the very essence of love, or a painting which brings out the beauty of the human form that is far more than just skin deep, Euler's equation reaches down into the very depths of existence". What is it that makes Euler's identity, eiπ + 1 = 0, so special? In Euler's Pioneering Equation Robin Wilson shows how this simple, elegant, and profound formula links together perhaps the five most important numbers in mathematics, each associated with a story in themselves: the number 1, the basis of our counting system; the concept of zero, which was a major development in mathematics, and opened up the idea of negative numbers; π an irrational number, the basis for the measurement of circles; the exponential e, associated with exponential growth and logarithms; and the imaginary number i, the square root of -1, the basis of complex numbers. Following a chapter on each of the elements, Robin Wilson discusses how the startling relationship between them was established, including the several near misses to the discovery of the formula.

Euler's Pioneering Equation

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Publisher :
ISBN 13 : 0198794932
Total Pages : 170 pages
Book Rating : 4.1/5 (987 download)

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Book Synopsis Euler's Pioneering Equation by : Robin Wilson

Download or read book Euler's Pioneering Equation written by Robin Wilson and published by . This book was released on 2019-07-17 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt: In just seven symbols, with profound and beautiful simplicity, Euler's Equation connects five of the most important numbers in mathematics. Robin Wilson explores each number in turn, then brings them together to consider the power of the equation as a whole.

A Most Elegant Equation

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Publisher : Basic Books
ISBN 13 : 0465093787
Total Pages : 240 pages
Book Rating : 4.4/5 (65 download)

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Book Synopsis A Most Elegant Equation by : David Stipp

Download or read book A Most Elegant Equation written by David Stipp and published by Basic Books. This book was released on 2017-11-07 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: An award-winning science writer introduces us to mathematics using the extraordinary equation that unites five of mathematics' most important numbers Bertrand Russell wrote that mathematics can exalt "as surely as poetry." This is especially true of one equation: ei(pi) + 1 = 0, the brainchild of Leonhard Euler, the Mozart of mathematics. More than two centuries after Euler's death, it is still regarded as a conceptual diamond of unsurpassed beauty. Called Euler's identity or God's equation, it includes just five numbers but represents an astonishing revelation of hidden connections. It ties together everything from basic arithmetic to compound interest, the circumference of a circle, trigonometry, calculus, and even infinity. In David Stipp's hands, Euler's identity formula becomes a contemplative stroll through the glories of mathematics. The result is an ode to this magical field.

Love and Math

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Publisher : Basic Books
ISBN 13 : 0465069959
Total Pages : 314 pages
Book Rating : 4.4/5 (65 download)

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Book Synopsis Love and Math by : Edward Frenkel

Download or read book Love and Math written by Edward Frenkel and published by Basic Books. This book was released on 2013-10-01 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: An awesome, globe-spanning, and New York Times bestselling journey through the beauty and power of mathematics What if you had to take an art class in which you were only taught how to paint a fence? What if you were never shown the paintings of van Gogh and Picasso, weren't even told they existed? Alas, this is how math is taught, and so for most of us it becomes the intellectual equivalent of watching paint dry. In Love and Math, renowned mathematician Edward Frenkel reveals a side of math we've never seen, suffused with all the beauty and elegance of a work of art. In this heartfelt and passionate book, Frenkel shows that mathematics, far from occupying a specialist niche, goes to the heart of all matter, uniting us across cultures, time, and space. Love and Math tells two intertwined stories: of the wonders of mathematics and of one young man's journey learning and living it. Having braved a discriminatory educational system to become one of the twenty-first century's leading mathematicians, Frenkel now works on one of the biggest ideas to come out of math in the last 50 years: the Langlands Program. Considered by many to be a Grand Unified Theory of mathematics, the Langlands Program enables researchers to translate findings from one field to another so that they can solve problems, such as Fermat's last theorem, that had seemed intractable before. At its core, Love and Math is a story about accessing a new way of thinking, which can enrich our lives and empower us to better understand the world and our place in it. It is an invitation to discover the magic hidden universe of mathematics.

In Pursuit of the Unknown

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Publisher : Basic Books
ISBN 13 : 0465029744
Total Pages : 247 pages
Book Rating : 4.4/5 (65 download)

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Book Synopsis In Pursuit of the Unknown by : Ian Stewart

Download or read book In Pursuit of the Unknown written by Ian Stewart and published by Basic Books. This book was released on 2012-03-13 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt: The seventeen equations that form the basis for life as we know it. Most people are familiar with history's great equations: Newton's Law of Gravity, for instance, or Einstein's theory of relativity. But the way these mathematical breakthroughs have contributed to human progress is seldom appreciated. In In Pursuit of the Unknown, celebrated mathematician Ian Stewart untangles the roots of our most important mathematical statements to show that equations have long been a driving force behind nearly every aspect of our lives. Using seventeen of our most crucial equations -- including the Wave Equation that allowed engineers to measure a building's response to earthquakes, saving countless lives, and the Black-Scholes model, used by bankers to track the price of financial derivatives over time -- Stewart illustrates that many of the advances we now take for granted were made possible by mathematical discoveries. An approachable, lively, and informative guide to the mathematical building blocks of modern life, In Pursuit of the Unknown is a penetrating exploration of how we have also used equations to make sense of, and in turn influence, our world.

Elements of Algebra

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Publisher :
ISBN 13 :
Total Pages : 960 pages
Book Rating : 4.:/5 (318 download)

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Book Synopsis Elements of Algebra by : Leonhard Euler

Download or read book Elements of Algebra written by Leonhard Euler and published by . This book was released on 1810 with total page 960 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Euler Through Time

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Publisher : American Mathematical Soc.
ISBN 13 : 0821835807
Total Pages : 312 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Euler Through Time by : V. S. Varadarajan

Download or read book Euler Through Time written by V. S. Varadarajan and published by American Mathematical Soc.. This book was released on 2006 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: Euler is one of the greatest and most prolific mathematicians of all time. He wrote the first accessible books on calculus, created the theory of circular functions, and discovered new areas of research such as elliptic integrals, the calculus of variations, graph theory, divergent series, and so on. It took hundreds of years for his successors to develop in full the theories he began, and some of his themes are still at the center of today's mathematics. It is of great interesttherefore to examine his work and its relation to current mathematics. This book attempts to do that. In number theory the discoveries he made empirically would require for their eventual understanding such sophisticated developments as the reciprocity laws and class field theory. His pioneering work onelliptic integrals is the precursor of the modern theory of abelian functions and abelian integrals. His evaluation of zeta and multizeta values is not only a fantastic and exciting story but very relevant to us, because they are at the confluence of much research in algebraic geometry and number theory today (Chapters 2 and 3 of the book). Anticipating his successors by more than a century, Euler created a theory of summation of series that do not converge in the traditional manner. Chapter 5of the book treats the progression of ideas regarding divergent series from Euler to many parts of modern analysis and quantum physics. The last chapter contains a brief treatment of Euler products. Euler discovered the product formula over the primes for the zeta function as well as for a smallnumber of what are now called Dirichlet $L$-functions. Here the book goes into the development of the theory of such Euler products and the role they play in number theory, thus offering the reader a glimpse of current developments (the Langlands program).

Dr. Euler's Fabulous Formula

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Publisher : Princeton University Press
ISBN 13 : 0691175918
Total Pages : 416 pages
Book Rating : 4.6/5 (911 download)

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Book Synopsis Dr. Euler's Fabulous Formula by : Paul J. Nahin

Download or read book Dr. Euler's Fabulous Formula written by Paul J. Nahin and published by Princeton University Press. This book was released on 2017-04-04 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the mid-eighteenth century, Swiss-born mathematician Leonhard Euler developed a formula so innovative and complex that it continues to inspire research, discussion, and even the occasional limerick. Dr. Euler's Fabulous Formula shares the fascinating story of this groundbreaking formula—long regarded as the gold standard for mathematical beauty—and shows why it still lies at the heart of complex number theory. In some ways a sequel to Nahin's An Imaginary Tale, this book examines the many applications of complex numbers alongside intriguing stories from the history of mathematics. Dr. Euler's Fabulous Formula is accessible to any reader familiar with calculus and differential equations, and promises to inspire mathematicians for years to come.

The Penguin Dictionary of Curious and Interesting Numbers

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Publisher : Penguin
ISBN 13 : 9780140261493
Total Pages : 260 pages
Book Rating : 4.2/5 (614 download)

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Book Synopsis The Penguin Dictionary of Curious and Interesting Numbers by : David Wells

Download or read book The Penguin Dictionary of Curious and Interesting Numbers written by David Wells and published by Penguin. This book was released on 1997-09-04 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides information on numbers and what makes particular ones noteworthy

How Euler Did Even More

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Publisher : The Mathematical Association of America
ISBN 13 : 0883855844
Total Pages : 254 pages
Book Rating : 4.8/5 (838 download)

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Book Synopsis How Euler Did Even More by : C. Edward Sandifer

Download or read book How Euler Did Even More written by C. Edward Sandifer and published by The Mathematical Association of America. This book was released on 2014-11-19 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sandifer has been studying Euler for decades and is one of the world’s leading experts on his work. This volume is the second collection of Sandifer’s “How Euler Did It” columns. Each is a jewel of historical and mathematical exposition. The sum total of years of work and study of the most prolific mathematician of history, this volume will leave you marveling at Euler’s clever inventiveness and Sandifer’s wonderful ability to explicate and put it all in context.

The Great Mathematicians

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Publisher : Arcturus Publishing
ISBN 13 : 1848589484
Total Pages : 294 pages
Book Rating : 4.8/5 (485 download)

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Book Synopsis The Great Mathematicians by : Raymond Flood

Download or read book The Great Mathematicians written by Raymond Flood and published by Arcturus Publishing. This book was released on 2012-06-01 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: Why did Florence Nightingale introduce pie charts? How did Lewis Carroll regard Pythagoras? Who learned calculus from her nursery wallpaper? Spanning from the ancient world to the modern age, The Great Mathematicians tells fascinating and unusual tales of the men and women who transformed mathematics. We meet the mathematician who knew eight languages by the time he was 11, the one who was sent to jail for gambling and the one who published a lot yet never existed. As well as providing rich bibliographic detail, Professors Raymond Flood and Robin Wilson explain various theorems using concise and accessible language. These include the Pythagorean theorem, Gödel's Incompleteness theorem, Fermat's Last Theorem and many more. Flood and Wilson are both former presidents of the British Society for the History of Mathematics and are uniquely qualified to lay out this incredible tale. This entertaining and rigorously accurate book presents mathematics with a human face, celebrating the achievements of the greatest mathematicians across history.

The Legacy of Leonhard Euler

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Publisher : World Scientific
ISBN 13 : 1848165269
Total Pages : 420 pages
Book Rating : 4.8/5 (481 download)

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Book Synopsis The Legacy of Leonhard Euler by : Lokenath Debnath

Download or read book The Legacy of Leonhard Euler written by Lokenath Debnath and published by World Scientific. This book was released on 2010 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book primarily serves as a historical research monograph on the biographical sketch and career of Leonhard Euler and his major contributions to numerous areas in the mathematical and physical sciences. It contains fourteen chapters describing Euler''s works on number theory, algebra, geometry, trigonometry, differential and integral calculus, analysis, infinite series and infinite products, ordinary and elliptic integrals and special functions, ordinary and partial differential equations, calculus of variations, graph theory and topology, mechanics and ballistic research, elasticity and fluid mechanics, physics and astronomy, probability and statistics. The book is written to provide a definitive impression of Euler''s personal and professional life as well as of the range, power, and depth of his unique contributions. This tricentennial tribute commemorates Euler the great man and Euler the universal mathematician of all time. Based on the author''s historically motivated method of teaching, special attention is given to demonstrate that Euler''s work had served as the basis of research and developments of mathematical and physical sciences for the last 300 years. An attempt is also made to examine his research and its relation to current mathematics and science. Based on a series of Euler''s extraordinary contributions, the historical development of many different subjects of mathematical sciences is traced with a linking commentary so that it puts the reader at the forefront of current research. Erratum. Sample Chapter(s). Chapter 1: Mathematics Before Leonhard Euler (434 KB). Contents: Mathematics Before Leonhard Euler; Brief Biographical Sketch and Career of Leonhard Euler; Euler''s Contributions to Number Theory and Algebra; Euler''s Contributions to Geometry and Spherical Trigonometry; Euler''s Formula for Polyhedra, Topology and Graph Theory; Euler''s Contributions to Calculus and Analysis; Euler''s Contributions to the Infinite Series and the Zeta Function; Euler''s Beta and Gamma Functions and Infinite Products; Euler and Differential Equations; The Euler Equations of Motion in Fluid Mechanics; Euler''s Contributions to Mechanics and Elasticity; Euler''s Work on the Probability Theory; Euler''s Contributions to Ballistics; Euler and His Work on Astronomy and Physics. Readership: Undergraduate and graduate students of mathematics, mathematics education, physics, engineering and science. As well as professionals and prospective mathematical scientists.

Applied Mathematics: A Very Short Introduction

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Publisher : Oxford University Press
ISBN 13 : 0191068888
Total Pages : 169 pages
Book Rating : 4.1/5 (91 download)

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Book Synopsis Applied Mathematics: A Very Short Introduction by : Alain Goriely

Download or read book Applied Mathematics: A Very Short Introduction written by Alain Goriely and published by Oxford University Press. This book was released on 2018-02-13 with total page 169 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics is playing an increasing important role in society and the sciences, enhancing our ability to use models and handle data. While pure mathematics is mostly interested in abstract structures, applied mathematics sits at the interface between this abstract world and the world in which we live. This area of mathematics takes its nourishment from society and science and, in turn, provides a unified way to understand problems arising in diverse fields. This Very Short Introduction presents a compact yet comprehensive view of the field of applied mathematics, and explores its relationships with (pure) mathematics, science, and engineering. Explaining the nature of applied mathematics, Alain Goriely discusses its early achievements in physics and engineering, and its development as a separate field after World War II. Using historical examples, current applications, and challenges, Goriely illustrates the particular role that mathematics plays in the modern sciences today and its far-reaching potential. ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.

Fashion, Faith, and Fantasy in the New Physics of the Universe

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Publisher : Princeton University Press
ISBN 13 : 1400880289
Total Pages : 520 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Fashion, Faith, and Fantasy in the New Physics of the Universe by : Roger Penrose

Download or read book Fashion, Faith, and Fantasy in the New Physics of the Universe written by Roger Penrose and published by Princeton University Press. This book was released on 2016-09-13 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the world's leading physicists questions some of the most fashionable ideas in physics today, including string theory What can fashionable ideas, blind faith, or pure fantasy possibly have to do with the scientific quest to understand the universe? Surely, theoretical physicists are immune to mere trends, dogmatic beliefs, or flights of fancy? In fact, acclaimed physicist and bestselling author Roger Penrose argues that researchers working at the extreme frontiers of physics are just as susceptible to these forces as anyone else. In this provocative book, he argues that fashion, faith, and fantasy, while sometimes productive and even essential in physics, may be leading today's researchers astray in three of the field's most important areas—string theory, quantum mechanics, and cosmology. Arguing that string theory has veered away from physical reality by positing six extra hidden dimensions, Penrose cautions that the fashionable nature of a theory can cloud our judgment of its plausibility. In the case of quantum mechanics, its stunning success in explaining the atomic universe has led to an uncritical faith that it must also apply to reasonably massive objects, and Penrose responds by suggesting possible changes in quantum theory. Turning to cosmology, he argues that most of the current fantastical ideas about the origins of the universe cannot be true, but that an even wilder reality may lie behind them. Finally, Penrose describes how fashion, faith, and fantasy have ironically also shaped his own work, from twistor theory, a possible alternative to string theory that is beginning to acquire a fashionable status, to "conformal cyclic cosmology," an idea so fantastic that it could be called "conformal crazy cosmology." The result is an important critique of some of the most significant developments in physics today from one of its most eminent figures.

Leonhard Euler

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Publisher : Princeton University Press
ISBN 13 : 0691196400
Total Pages : 689 pages
Book Rating : 4.6/5 (911 download)

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Book Synopsis Leonhard Euler by : Ronald S. Calinger

Download or read book Leonhard Euler written by Ronald S. Calinger and published by Princeton University Press. This book was released on 2019-12-03 with total page 689 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This is the first full-scale biography of Leonhard Euler (1707-83), one of the greatest mathematicians and theoretical physicists of all time. In this comprehensive and authoritative account, Ronald Calinger connects the story of Euler's eventful life to the astonishing achievements that place him in the company of Archimedes, Newton, and Gauss. Drawing chiefly on Euler's massive published works and correspondence, which fill more than eighty volumes so far, this biography sets Euler's work in its multilayered context--personal, intellectual, institutional, political, cultural, religious, and social. It is a story of nearly incessant accomplishment, from Euler's fundamental contributions to almost every area of pure and applied mathematics--especially calculus, number theory, notation, optics, and celestial, rational, and fluid mechanics--to his advancements in shipbuilding, telescopes, ballistics, cartography, chronology, and music theory. The narrative takes the reader from Euler's childhood and education in Basel through his first period in St. Petersburg, 1727-41, where he gained a European reputation by solving the Basel problem and systematically developing analytical mechanics. Invited to Berlin by Frederick II, Euler published his famous Introductio in analysin infinitorum, devised continuum mechanics, and proposed a pulse theory of light. Returning to St. Petersburg in 1766, he created the analytical calculus of variations, developed the most precise lunar theory of the time that supported Newton's dynamics, and published the best-selling Letters to a German Princess--all despite eye problems that ended in near-total blindness. In telling the remarkable story of Euler and how his achievements brought pan-European distinction to the Petersburg and Berlin academies of sciences, the book also demonstrates with new depth and detail the central role of mathematics in the Enlightenment."--Publisher's description.

Leonhard Euler

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Publisher : Elsevier
ISBN 13 : 9780080471297
Total Pages : 542 pages
Book Rating : 4.4/5 (712 download)

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Book Synopsis Leonhard Euler by : Robert E. Bradley

Download or read book Leonhard Euler written by Robert E. Bradley and published by Elsevier. This book was released on 2007-03-20 with total page 542 pages. Available in PDF, EPUB and Kindle. Book excerpt: The year 2007 marks the 300th anniversary of the birth of one of the Enlightenment’s most important mathematicians and scientists, Leonhard Euler. This volume is a collection of 24 essays by some of the world’s best Eulerian scholars from seven different countries about Euler, his life and his work. Some of the essays are historical, including much previously unknown information about Euler’s life, his activities in the St. Petersburg Academy, the influence of the Russian Princess Dashkova, and Euler’s philosophy. Others describe his influence on the subsequent growth of European mathematics and physics in the 19th century. Still others give technical details of Euler’s innovations in probability, number theory, geometry, analysis, astronomy, mechanics and other fields of mathematics and science. - Over 20 essays by some of the best historians of mathematics and science, including Ronald Calinger, Peter Hoffmann, Curtis Wilson, Kim Plofker, Victor Katz, Ruediger Thiele, David Richeson, Robin Wilson, Ivor Grattan-Guinness and Karin Reich - New details of Euler's life in two essays, one by Ronald Calinger and one he co-authored with Elena Polyakhova - New information on Euler's work in differential geometry, series, mechanics, and other important topics including his influence in the early 19th century

Mathematicians

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Publisher :
ISBN 13 :
Total Pages : 212 pages
Book Rating : 4.3/5 (97 download)

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Book Synopsis Mathematicians by : Mariana Cook

Download or read book Mathematicians written by Mariana Cook and published by . This book was released on 2009-06-21 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: Photographs accompanied by autobiographical text written by each mathematician.